On Feb 7, 7:28 pm, WM <mueck...@rz.fh-augsburg.de> wrote:> On 7 Feb., 19:14, William Hughes <wpihug...@gmail.com> wrote:>>>>>>>>>> > On Feb 7, 5:57 pm, WM <mueck...@rz.fh-augsburg.de> wrote:>> > > On 7 Feb., 15:56, William Hughes <wpihug...@gmail.com> wrote:>> > > > On Feb 7, 3:25 pm, WM <mueck...@rz.fh-augsburg.de> wrote:>> > > > <snip>>> > > > >... a subset S of the countable set F of finite words bijects with> > > > > the set D of definable numbers>> > > by definition.>> > > > Nope. Every D corresponds to some finite word.>> > > No, D is a set or at least a collection. A definable number is an> > > element of D.>> > > > However, S,> > > > the collection of all the correspondences, may not be a subset> > > > of F (subsets must be computable).>> > > Need not be a subset. It is sufficient to know that there are not more> > > than countably many correspondences,>> > There is no set of correspondences thus there is no number> > of correspondences. You cannot know anything about> > the number of correspondences.->> You are in error again. There is the axiom of power set. For any F,> there is P such that D e P if and only if D c F. According to it every> subset of the countable set F exists. Will you dispute that the finite> definitions of numbers are a subset of F?